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A playground for exploring 3-manifold groups
by
William Floyd
Virginia Tech
Coauthors: James Cannon (Brigham Young University), Walter Parry (Eastern Michigan University)
Given a face-pairing (with each map orientation-reversing) on a faceted 3-ball P, the technique of twisted face-pairing gives an infinite parametrized family of face-pairings on subdivisions of P. For each element of the family, the quotient complex is a closed 3-manifold. From the input, one can mechanically give a presentation for its fundamental group.
The talk will concentrate on examples. It is spectacularly easy to construct Gromov hyperbolic 3-manifold groups from this construction, and we have constructed examples from five of Thurston's eight 3-dimensional geometries. One can use the construction in conjunction with SnapPea to easily explore many 3-manifolds and their groups.
Date received: February 1, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadu-04.